Using results relating the complexity of a two dimensional sub-shift to its periodicity, we obtain an application to the well-known conjecture of Furstenberg on a Borel probability measure on [0, 1) which is invariant under both x → px (mod 1) and x → qx (mod 1), showing that any potential counterexample has a nontrivial lower bound on its complexity.
|Original language||English (US)|
|Number of pages||11|
|Journal||Proceedings of the American Mathematical Society|
|State||Published - 2017|
ASJC Scopus subject areas
- Applied Mathematics